What is the value of (tan(45)+tan(15))/(1-tan(45)tan(15)) ?

The value of (tan(45)+tan(15))/(1-tan(45)tan(15)) is square root of 3

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(tan(45)+tan(15))/(1-tan(45)tan(15))

\frac{tan ( 4 5 ^{\circ} ) + tan ( 1 5 ^{\circ} )}{1 - tan ( 4 5 ^{\circ} ) tan ( 1 5 ^{\circ} )}

3

Solution steps

\frac{tan ( 4 5 ^{\circ} ) + tan ( 1 5 ^{\circ} )}{1 - tan ( 4 5 ^{\circ} ) tan ( 1 5 ^{\circ} )}

Use the following trivial identity:

tan (4 5^{\circ}) = 1

Rewrite using trig identities:

tan (1 5^{\circ}) = 2 - 3

= \frac{1 + 2 - 3}{1 - 1 \cdot ( 2 - 3 )}

Simplify

\frac{1 + 2 - 3}{1 - 1 \cdot ( 2 - 3 )} : 3

= 3

cos^{2} (2 8^{\circ}) - sin^{2} (2 8^{\circ})

arccos (- 0.34)

arccos (- 0.75)

arccos (- 0.62)

sinh (- 2)

What is the value of (tan(45)+tan(15))/(1-tan(45)tan(15)) ?
The value of (tan(45)+tan(15))/(1-tan(45)tan(15)) is square root of 3